St. Lawrence University
2024-04-26
Johnson, A. A., Ott, M. Q., & Dogucu, M. (2021). Bayes Rules! An Introduction to Applied Bayesian Modeling
\[ \text{logit}(\pi_{ijk}) = \beta_{alcaraz}X_{alcaraz} + \beta_{sinner}X_{sinner} + \ldots + \beta_{ruud}X_{ruud}, \]
\[\begin{equation} \begin{aligned} \text{logit}(\pi_{ij}) & = \beta_{alcaraz}(1) + \beta_{sinner}(-1) + \ldots + \beta_{ruud}(0) \\ & = \beta_{alcaraz} - \beta_{sinner} \end{aligned} \end{equation}\]
\[\begin{equation} \begin{aligned} \text{logit}(\pi_{ijk}) = & \beta_{alcaraz}X_{alcaraz} + \beta_{sinner}X_{sinner} + \ldots + \beta_{ruud}X_{ruud} + \\ & \alpha_{alcaraz}X_{alcaraz,s} + \alpha_{sinner}X_{sinner,s} + \ldots + \alpha_{ruud}X_{ruud,s} \end{aligned} \end{equation}\]
\[\begin{equation} \begin{aligned} \text{logit}(\pi_{ijk}) & = \beta_{alcaraz}(1) + \beta_{sinner}(-1) + \ldots + \beta_{ruud}(0) + \\ & \;\;\;\; \alpha_{alcaraz}(1) + \alpha_{sinner}(0) + \ldots + \alpha_{ruud}(0) \\ & = \beta_{alcaraz} + \alpha_{alcaraz} - \beta_{sinner} \end{aligned} \end{equation}\]
\[\begin{equation} \begin{aligned} \text{logit}(\pi_{ijk}) & = \beta_{alcaraz}(1) + \beta_{sinner}(-1) + \ldots + \beta_{ruud}(0) + \\ & \;\;\;\; \alpha_{alcaraz}(0) + \alpha_{sinner}(-1) + \ldots + \alpha_{ruud}(0) \\ & = \beta_{alcaraz} - \beta_{sinner} - \alpha_{sinner} \end{aligned} \end{equation}\]
We are looking at 3 different probabilities
Dynamic Nature
Data-driven Insights
Future Directions
deuce packageTennis In-Match Win Prediction